Goal:

In this experiment I am observing a “co-evolving” population with a non-heritable trait. I will break my simulation and make the trait a random draw (rnorm(1, 3, 2)). Newts and snakes will still interact, but their phenotype will be determined by this random draw. This random draw should create a mean phenotype near 1.

Questions:

What happens when a co-evolving trait is not heritable? Can the two species co-evolve? With there be spatial correlation? What will the cost function do to newt and snake phenotypes?

Background

In my regular co-evolution experimental simulations newts and snakes have a phenotype based on mutations and their effect sizes. When newts and snakes interact the species that has a higher phenotype is deemed a “winner” and survives, while the other one dies. Over many interactions and generations newts and snakes co-evolve. The phenotype of newts and snakes typically increase. However, unlike the real newts and snakes I have yet to see consistent high levels of spatial correlation. I am running further experiments to get a better of how different aspects of my system (heritability and interaction) can affect phenotype and spatial correlation. In this experiment I take away the ability for a phenotype to be inherited. I predict that there will be no spatial phenotype correlation and no phenotype increase.

## All cor, lit, and grid files exist!
## This program will now end!

The Data

I ran four trials per GA combination (I look back and find this unnecessarily, because phenotype is reassigned to be a random draw). After running my simulations, I gathered my data into three files; data containing a mean value for the entire map (lit), correlation data based off of local populations that were divided into grids (cor) and data collected from grid based populations (grid). These simulations have a msprime (coalescent/burn in/random genetic variation) and then run for 50,000 generations in SLiM (co-evolution) (all with the same GA values).

GA1 experiment values:

Landscape: 20 by 5 grid. A tall map!: 35*4 H, 35 W

Mean Phenotype Whole Simulation

The first result I will look at is a plot of how the mean phenotype of the entire population of newts and snakes changes overtime. Each of these plots has three colored lines, red for the mean newt phenotype, blue for the mean snake phenotype, and black for the difference between mean snake and mean newt phenotype. Mutational variance increases for the snakes as you go down the figure (top to bottom) and increases for the newts as you go across (left to right). The table represents the average difference between mean snake phenotype and mean newt phenotype between the four trials.

Phenotype differences

Table of average Differences

##                    Group.1             x
## 1  1e-08_0.005_1e-08_0.005 -9.974248e-05
## 2   1e-08_0.005_1e-09_0.05  1.927856e-05
## 3    1e-08_0.005_1e-10_0.5 -1.040982e-05
## 4      1e-08_0.005_1e-11_5 -1.221172e-04
## 5   1e-09_0.05_1e-08_0.005 -8.962224e-05
## 6    1e-09_0.05_1e-09_0.05 -1.314459e-04
## 7     1e-09_0.05_1e-10_0.5 -4.893687e-05
## 8       1e-09_0.05_1e-11_5 -1.299599e-05
## 9    1e-10_0.5_1e-08_0.005  7.246493e-05
## 10    1e-10_0.5_1e-09_0.05 -8.737675e-05
## 11     1e-10_0.5_1e-10_0.5 -2.912826e-05
## 12       1e-10_0.5_1e-11_5 -1.236082e-04
## 13     1e-11_5_1e-08_0.005  4.427355e-05
## 14      1e-11_5_1e-09_0.05  1.431764e-05
## 15       1e-11_5_1e-10_0.5 -9.227655e-05
## 16         1e-11_5_1e-11_5  9.899800e-07

The average newt and snake phenotype over time in this experiment is 1. There is pretty much no difference between snake and newt phenotypes. The GA has no influence on the newt and snake phenotype.

Connection between higher phenotype and population

In my previous simulations, I saw a relationship between population size and phenotype. Species with a higher phenotype often had a higher population size (except that snakes had a slightly larger population size when the phenotypes where equal). Here, I will plot newt population size by snake population size with the points color indicating the difference between mean snake and mean newt phenotype (blue=snakes, red=newts have a higher phenotype). I also plot histograms of the differences between snake and newt population size (green) and phenotype (purple). To get these histogram on the same plot I devied population size by 1000.

Phenotype differences

Phenotype & Populationsize differences

The phenotype difference plot indicates that there is a relationship between newt ans snake population, but no relationship to phenotype. When snakes have a larger population size newts tend to have a smaller population size and vise-versa. The differences between newt and snake phenotype is very small. In the histograms snakes tend to have a larger population size for a majority of the simulation (eyeballing mean is around 500). Again, there is no difference between snake and newt mean phenotype. There is no GA impact seen in either of these figures.

Correlation

In this next section I look at spatial correlation. Spatial correlation could be positive, negative, or near 0. It is positive when both species are high or low in different areas. It is negative when the species are high/low and low/high. And it is near 0 when there is no relationship between the two phenotypes.

After looking at this figure, I can see that there is a very small range of correlation values, centered around 0. None few reach (or come near) the real newt-snake correlation. Wheb these trats are not be inherited this make

Correlation Histograms

In order to understand how spatial correlations where changing with time I took 5,000 generation time slices to look at all four trials correlation values. Each color is a different trial per GA combination. The histogram values are stacked with each value being a single measurement at a particular time point.

Plot 1

Plot 2

Plot 3

Plot 4

Plot 5

Plot 6

Plot 7

Plot 8

Plot 9

Plot 10

All plots look the same. All correlations are centered around 0 and do not go past +/- 0.5. There are no strong correlations. I can conclude that there would be no random correlations when newt and snake phenotype is drawn at random. A good subsequent experiment would be to make one of these phenotype heritable and the other not. Could this situation lead to high spatial correlations or a high phenotype.

Correlation across time

In this next section I look at the mean newt/snake phenotype (red/blue) and spatial correlation (pink) across time for all GAs. Below we will look at 3 randomly chosen results.

Random 1

## [1] "pattern 1e-08_0.005_1e-10_0.5_1"
## [1] "Cor between average snake pheno and local cor 0.0123103551191899"
## [1] "Cor between average newt pheno and local cor -0.00714843953880616"
## [1] "Cor between average dif pheno and local cor 0.0136349959505177"
## [1] "Cor between newt pheno and snake -0.00410050210119346"

Random 2

## [1] "pattern 1e-09_0.05_1e-09_0.05_0"
## [1] "Cor between average snake pheno and local cor -0.0156548773932808"
## [1] "Cor between average newt pheno and local cor -0.0178843730762579"
## [1] "Cor between average dif pheno and local cor 0.00196128700061584"
## [1] "Cor between newt pheno and snake 0.00316282264027713"

Random 3

## [1] "pattern 1e-08_0.005_1e-10_0.5_0"
## [1] "Cor between average snake pheno and local cor -0.0277794142998846"
## [1] "Cor between average newt pheno and local cor -0.00764766864866953"
## [1] "Cor between average dif pheno and local cor -0.0133059757857941"
## [1] "Cor between newt pheno and snake -0.00444227640341161"

Each of these randomly chosen simulation results look very similar. The mean phenotypes of newts and snake jump around every generation, which creates a very fuzzy caterpillar look. The newt and snake spatial phenotype correlation hovers around 0. There are a few instances where it gets close to +/- 0.5, but never crosses. The spatial correlation also jumps around (does not continue in a strait line).

What happens over time (looking at the beginning, middle, and late part of my simulations)

This next section is just getting a glimpse at how newt & snake phenotype and population size differ over time. The populations start off with about 250 individuals each. Each individual has a different genetic background created from msprime. In this experiment phenotypes where not heritable, each individual had a randomly chose phenotype (from a normal distribution). The plots that follow will show two things; 1) newt by snake population size with each dot repersenting the difference between snake and newt mean phenotype (blue=snake has a higher phenotype/ red=newt has a higher phenotype), and 2) histograms of the difference between snake and newt phenotype and population size (purple and green, respectively).

Pheno Beginning

Pheno Middle

Pheno End

Dif Beginning

Dif Middle

Dif End

From these results, I can tell that there is a relationship between newt and snake population size. Snakes tend to have a larger population size even when the snake and newt phenotypes are even. This is likely caused by the increase in fitness when a newt is successfully eaten. The phenotypes are very random.

Summary

The next section of plots contain my main summaries about GA. There are four types of plots; plots 1 & 2 observe patterns caused by newt and snake GA when comparing newt population size by snake population size and the difference between snake and newt mean phenotype by snake population size, plots 3 & 4 take a deeper look to see if the GA of snake or newt affects the difference between phenotypes. In these four types of plots I will at the beginning, middle, and end of my simulation. The color of the points is snake GA and the shape of the points is newt GA. The combination of shape and color is the GA of that particular simulation. There are for trial (points) for each GA combination.

Early-Sim Population Size Summary

Mid-Sim Population Size Summary

Late-Sim Population Size Summary

Early Difference Summary

Mid Difference Summary

Late Difference Summary

By Snake GA (Early)

By Snake GA (Mid)

By Snake GA (Late)

By Newt GA (Early)

By Newt GA (Mid)

By Newt GA (Late)

These plots confirm that there no relationship between GA and phenotype. There is a relationship between snake and newt population. When snake population size is high newt population size is smaller. When newts have a high population size, snake population size is smaller. These figures show that snakes will tend to have a larger population size when the newt and snake phenotypes are about even.

Heatmap

The heatmap section is a different visual representation of the mean snake population size or snake-newt phenotype difference of a time slice. There will be two plots at different time stages (beginning, middle, and end of my simulation). One plot will show the average snake population size with yellow being a high population size and purple being low population size. The figure will show the difference between mean snake and newt phenotype, where blue indicated that snakes have a higher phenotype and red indicates that newts have a higher phenotype. The x-axis of these plots is the newt GA. The y-axis of these plots are the snake GA and trial number. Each figure should be read in groups of 4 (matching snake GA).

Population Size (Early)

Population Size (Mid)

Population Size (Late)

Phenotype (Early)

Phenotype (Mid)

Phenotype (Late)

There is very little agreement between trials in both snake population size and phenotype differences. Most colors tend to be in the center of the two extremes. The results change drastically between each of the time slices.

What is up with the correlations

This sections takes a more in depth view of how newt and snake phenotype can be correlated on a local level. I look at the mean phenotype, phenotype standard deviation (sd), max phenotype, min phenotype, and population of newts and snakes for a time point at the beginning, middle and end of my simulation. Each plot shows a local average of my test parameter (mean, sd, max, …) for a smaller area of my larger map. Newt are represented by circles, and snake are represented by squares. Graphs with a phenotype parameter range from low (purple) through blue and green to a high (yellow). The population size figures range from low (purple) through pink and orange to a high (yellow). When not enough individuals where in an area the shape is colored grey. The second smaller plot in the figure shows the newt by snake on the current parameter with point color indication location (corner=pink, edge=green, middle=blue).

Early Simulation Correlation

Mean

## [1] -0.007116659

SD

## [1] -0.04331415

Max Phenotype

## [1] -0.2598047

Min Phenotype

## [1] -0.09258549

Population Size

## [1] -0.2482845

Middle Simulation Correlation

Mean

## [1] 0.03312796

SD

## [1] -0.02311899

Max Phenotype

## [1] 0.2616178

Min Phenotype

## [1] 0.07604557

Population Size

## [1] 0.5886762

Late Simulation Correlation

Mean

## [1] -0.04199475

SD

## [1] 0.2309632

Max Phenotype

## [1] 0.2136041

Min Phenotype

## [1] 0.07629167

Population Size

## [1] 0.4558851